/*
 * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
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 */

package com.nulldev.util.internal.backport.arrays;

/**
 * This class implements the Dual-Pivot Quicksort algorithm by Vladimir
 * Yaroslavskiy, Jon Bentley, and Josh Bloch. The algorithm offers O(n log(n))
 * performance on many data sets that cause other quicksorts to degrade to
 * quadratic performance, and is typically faster than traditional (one-pivot)
 * Quicksort implementations.
 *
 * All exposed methods are package-private, designed to be invoked from public
 * methods (in class Arrays) after performing any necessary array bounds checks
 * and expanding parameters into the required forms.
 *
 * @author Vladimir Yaroslavskiy
 * @author Jon Bentley
 * @author Josh Bloch
 *
 * @version 2011.02.11 m765.827.12i:5\7pm
 * @since 1.7
 */
final class DualPivotQuicksort {

	/**
	 * Prevents instantiation.
	 */
	private DualPivotQuicksort() {
	}

	/*
	 * Tuning parameters.
	 */

	/**
	 * The maximum number of runs in merge sort.
	 */
	private static final int MAX_RUN_COUNT = 67;

	/**
	 * The maximum length of run in merge sort.
	 */
	private static final int MAX_RUN_LENGTH = 33;

	/**
	 * If the length of an array to be sorted is less than this constant, Quicksort
	 * is used in preference to merge sort.
	 */
	private static final int QUICKSORT_THRESHOLD = 286;

	/**
	 * If the length of an array to be sorted is less than this constant, insertion
	 * sort is used in preference to Quicksort.
	 */
	private static final int INSERTION_SORT_THRESHOLD = 47;

	/**
	 * If the length of a byte array to be sorted is greater than this constant,
	 * counting sort is used in preference to insertion sort.
	 */
	private static final int COUNTING_SORT_THRESHOLD_FOR_BYTE = 29;

	/**
	 * If the length of a short or char array to be sorted is greater than this
	 * constant, counting sort is used in preference to Quicksort.
	 */
	private static final int COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR = 3200;

	/*
	 * Sorting methods for seven primitive types.
	 */

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(int[] a, int left, int right, int[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					int t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		int[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new int[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			int[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(int[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					int ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					int a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				int last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			int t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			int t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			int t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			int t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			int pivot1 = a[e2];
			int pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				int ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					int ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = pivot1;
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			int pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				int ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = pivot;
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(long[] a, int left, int right, long[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					long t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		long[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new long[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			long[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(long[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					long ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					long a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				long last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			long t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			long t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			long t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			long t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			long pivot1 = a[e2];
			long pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				long ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					long ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = pivot1;
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			long pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				long ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = pivot;
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(short[] a, int left, int right, short[] work, int workBase, int workLen) {
		// Use counting sort on large arrays
		if (right - left > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
			int[] count = new int[NUM_SHORT_VALUES];

			for (int i = left - 1; ++i <= right; count[a[i] - Short.MIN_VALUE]++)
				;
			for (int i = NUM_SHORT_VALUES, k = right + 1; k > left;) {
				while (count[--i] == 0)
					;
				short value = (short) (i + Short.MIN_VALUE);
				int s = count[i];

				do {
					a[--k] = value;
				} while (--s > 0);
			}
		} else { // Use Dual-Pivot Quicksort on small arrays
			doSort(a, left, right, work, workBase, workLen);
		}
	}

	/** The number of distinct short values. */
	private static final int NUM_SHORT_VALUES = 1 << 16;

	/**
	 * Sorts the specified range of the array.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	private static void doSort(short[] a, int left, int right, short[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					short t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		short[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new short[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			short[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(short[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					short ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					short a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				short last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			short t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			short t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			short t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			short t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			short pivot1 = a[e2];
			short pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				short ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					short ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = pivot1;
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			short pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				short ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = pivot;
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(char[] a, int left, int right, char[] work, int workBase, int workLen) {
		// Use counting sort on large arrays
		if (right - left > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
			int[] count = new int[NUM_CHAR_VALUES];

			for (int i = left - 1; ++i <= right; count[a[i]]++)
				;
			for (int i = NUM_CHAR_VALUES, k = right + 1; k > left;) {
				while (count[--i] == 0)
					;
				char value = (char) i;
				int s = count[i];

				do {
					a[--k] = value;
				} while (--s > 0);
			}
		} else { // Use Dual-Pivot Quicksort on small arrays
			doSort(a, left, right, work, workBase, workLen);
		}
	}

	/** The number of distinct char values. */
	private static final int NUM_CHAR_VALUES = 1 << 16;

	/**
	 * Sorts the specified range of the array.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	private static void doSort(char[] a, int left, int right, char[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					char t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		char[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new char[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			char[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(char[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					char ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					char a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				char last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			char t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			char t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			char t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			char t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			char pivot1 = a[e2];
			char pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				char ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					char ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = pivot1;
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			char pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				char ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = pivot;
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}

	/** The number of distinct byte values. */
	private static final int NUM_BYTE_VALUES = 1 << 8;

	/**
	 * Sorts the specified range of the array.
	 *
	 * @param a     the array to be sorted
	 * @param left  the index of the first element, inclusive, to be sorted
	 * @param right the index of the last element, inclusive, to be sorted
	 */
	static void sort(byte[] a, int left, int right) {
		// Use counting sort on large arrays
		if (right - left > COUNTING_SORT_THRESHOLD_FOR_BYTE) {
			int[] count = new int[NUM_BYTE_VALUES];

			for (int i = left - 1; ++i <= right; count[a[i] - Byte.MIN_VALUE]++)
				;
			for (int i = NUM_BYTE_VALUES, k = right + 1; k > left;) {
				while (count[--i] == 0)
					;
				byte value = (byte) (i + Byte.MIN_VALUE);
				int s = count[i];

				do {
					a[--k] = value;
				} while (--s > 0);
			}
		} else { // Use insertion sort on small arrays
			for (int i = left, j = i; i < right; j = ++i) {
				byte ai = a[i + 1];
				while (ai < a[j]) {
					a[j + 1] = a[j];
					if (j-- == left) {
						break;
					}
				}
				a[j + 1] = ai;
			}
		}
	}

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(float[] a, int left, int right, float[] work, int workBase, int workLen) {
		/*
		 * Phase 1: Move NaNs to the end of the array.
		 */
		while (left <= right && Float.isNaN(a[right])) {
			--right;
		}
		for (int k = right; --k >= left;) {
			float ak = a[k];
			if (ak != ak) { // a[k] is NaN
				a[k] = a[right];
				a[right] = ak;
				--right;
			}
		}

		/*
		 * Phase 2: Sort everything except NaNs (which are already in place).
		 */
		doSort(a, left, right, work, workBase, workLen);

		/*
		 * Phase 3: Place negative zeros before positive zeros.
		 */
		int hi = right;

		/*
		 * Find the first zero, or first positive, or last negative element.
		 */
		while (left < hi) {
			int middle = (left + hi) >>> 1;
			float middleValue = a[middle];

			if (middleValue < 0.0f) {
				left = middle + 1;
			} else {
				hi = middle;
			}
		}

		/*
		 * Skip the last negative value (if any) or all leading negative zeros.
		 */
		while (left <= right && Float.floatToRawIntBits(a[left]) < 0) {
			++left;
		}

		/*
		 * Move negative zeros to the beginning of the sub-range.
		 *
		 * Partitioning:
		 *
		 * +----------------------------------------------------+ | < 0.0 | -0.0 | 0.0 |
		 * ? ( >= 0.0 ) | +----------------------------------------------------+ ^ ^ ^ |
		 * | | left p k
		 *
		 * Invariants:
		 *
		 * all in (*, left) < 0.0 all in [left, p) == -0.0 all in [p, k) == 0.0 all in
		 * [k, right] >= 0.0
		 *
		 * Pointer k is the first index of ?-part.
		 */
		for (int k = left, p = left - 1; ++k <= right;) {
			float ak = a[k];
			if (ak != 0.0f) {
				break;
			}
			if (Float.floatToRawIntBits(ak) < 0) { // ak is -0.0f
				a[k] = 0.0f;
				a[++p] = -0.0f;
			}
		}
	}

	/**
	 * Sorts the specified range of the array.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	private static void doSort(float[] a, int left, int right, float[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					float t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		float[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new float[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			float[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(float[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					float ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					float a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				float last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			float t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			float t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			float t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			float t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			float pivot1 = a[e2];
			float pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				float ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					float ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = a[great];
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			float pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				float ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = a[great];
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}

	/**
	 * Sorts the specified range of the array using the given workspace array slice
	 * if possible for merging
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	static void sort(double[] a, int left, int right, double[] work, int workBase, int workLen) {
		/*
		 * Phase 1: Move NaNs to the end of the array.
		 */
		while (left <= right && Double.isNaN(a[right])) {
			--right;
		}
		for (int k = right; --k >= left;) {
			double ak = a[k];
			if (ak != ak) { // a[k] is NaN
				a[k] = a[right];
				a[right] = ak;
				--right;
			}
		}

		/*
		 * Phase 2: Sort everything except NaNs (which are already in place).
		 */
		doSort(a, left, right, work, workBase, workLen);

		/*
		 * Phase 3: Place negative zeros before positive zeros.
		 */
		int hi = right;

		/*
		 * Find the first zero, or first positive, or last negative element.
		 */
		while (left < hi) {
			int middle = (left + hi) >>> 1;
			double middleValue = a[middle];

			if (middleValue < 0.0d) {
				left = middle + 1;
			} else {
				hi = middle;
			}
		}

		/*
		 * Skip the last negative value (if any) or all leading negative zeros.
		 */
		while (left <= right && Double.doubleToRawLongBits(a[left]) < 0) {
			++left;
		}

		/*
		 * Move negative zeros to the beginning of the sub-range.
		 *
		 * Partitioning:
		 *
		 * +----------------------------------------------------+ | < 0.0 | -0.0 | 0.0 |
		 * ? ( >= 0.0 ) | +----------------------------------------------------+ ^ ^ ^ |
		 * | | left p k
		 *
		 * Invariants:
		 *
		 * all in (*, left) < 0.0 all in [left, p) == -0.0 all in [p, k) == 0.0 all in
		 * [k, right] >= 0.0
		 *
		 * Pointer k is the first index of ?-part.
		 */
		for (int k = left, p = left - 1; ++k <= right;) {
			double ak = a[k];
			if (ak != 0.0d) {
				break;
			}
			if (Double.doubleToRawLongBits(ak) < 0) { // ak is -0.0d
				a[k] = 0.0d;
				a[++p] = -0.0d;
			}
		}
	}

	/**
	 * Sorts the specified range of the array.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param work     a workspace array (slice)
	 * @param workBase origin of usable space in work array
	 * @param workLen  usable size of work array
	 */
	private static void doSort(double[] a, int left, int right, double[] work, int workBase, int workLen) {
		// Use Quicksort on small arrays
		if (right - left < QUICKSORT_THRESHOLD) {
			sort(a, left, right, true);
			return;
		}

		/*
		 * Index run[i] is the start of i-th run (ascending or descending sequence).
		 */
		int[] run = new int[MAX_RUN_COUNT + 1];
		int count = 0;
		run[0] = left;

		// Check if the array is nearly sorted
		for (int k = left; k < right; run[count] = k) {
			if (a[k] < a[k + 1]) { // ascending
				while (++k <= right && a[k - 1] <= a[k])
					;
			} else if (a[k] > a[k + 1]) { // descending
				while (++k <= right && a[k - 1] >= a[k])
					;
				for (int lo = run[count] - 1, hi = k; ++lo < --hi;) {
					double t = a[lo];
					a[lo] = a[hi];
					a[hi] = t;
				}
			} else { // equal
				for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) {
					if (--m == 0) {
						sort(a, left, right, true);
						return;
					}
				}
			}

			/*
			 * The array is not highly structured, use Quicksort instead of merge sort.
			 */
			if (++count == MAX_RUN_COUNT) {
				sort(a, left, right, true);
				return;
			}
		}

		// Check special cases
		// Implementation note: variable "right" is increased by 1.
		if (run[count] == right++) { // The last run contains one element
			run[++count] = right;
		} else if (count == 1) { // The array is already sorted
			return;
		}

		// Determine alternation base for merge
		byte odd = 0;
		for (int n = 1; (n <<= 1) < count; odd ^= 1)
			;

		// Use or create temporary array b for merging
		double[] b; // temp array; alternates with a
		int ao, bo; // array offsets from 'left'
		int blen = right - left; // space needed for b
		if (work == null || workLen < blen || workBase + blen > work.length) {
			work = new double[blen];
			workBase = 0;
		}
		if (odd == 0) {
			System.arraycopy(a, left, work, workBase, blen);
			b = a;
			bo = 0;
			a = work;
			ao = workBase - left;
		} else {
			b = work;
			ao = 0;
			bo = workBase - left;
		}

		// Merging
		for (int last; count > 1; count = last) {
			for (int k = (last = 0) + 2; k <= count; k += 2) {
				int hi = run[k], mi = run[k - 1];
				for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
					if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
						b[i + bo] = a[p++ + ao];
					} else {
						b[i + bo] = a[q++ + ao];
					}
				}
				run[++last] = hi;
			}
			if ((count & 1) != 0) {
				for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao])
					;
				run[++last] = right;
			}
			double[] t = a;
			a = b;
			b = t;
			int o = ao;
			ao = bo;
			bo = o;
		}
	}

	/**
	 * Sorts the specified range of the array by Dual-Pivot Quicksort.
	 *
	 * @param a        the array to be sorted
	 * @param left     the index of the first element, inclusive, to be sorted
	 * @param right    the index of the last element, inclusive, to be sorted
	 * @param leftmost indicates if this part is the leftmost in the range
	 */
	private static void sort(double[] a, int left, int right, boolean leftmost) {
		int length = right - left + 1;

		// Use insertion sort on tiny arrays
		if (length < INSERTION_SORT_THRESHOLD) {
			if (leftmost) {
				/*
				 * Traditional (without sentinel) insertion sort, optimized for server VM, is
				 * used in case of the leftmost part.
				 */
				for (int i = left, j = i; i < right; j = ++i) {
					double ai = a[i + 1];
					while (ai < a[j]) {
						a[j + 1] = a[j];
						if (j-- == left) {
							break;
						}
					}
					a[j + 1] = ai;
				}
			} else {
				/*
				 * Skip the longest ascending sequence.
				 */
				do {
					if (left >= right) {
						return;
					}
				} while (a[++left] >= a[left - 1]);

				/*
				 * Every element from adjoining part plays the role of sentinel, therefore this
				 * allows us to avoid the left range check on each iteration. Moreover, we use
				 * the more optimized algorithm, so called pair insertion sort, which is faster
				 * (in the context of Quicksort) than traditional implementation of insertion
				 * sort.
				 */
				for (int k = left; ++left <= right; k = ++left) {
					double a1 = a[k], a2 = a[left];

					if (a1 < a2) {
						a2 = a1;
						a1 = a[left];
					}
					while (a1 < a[--k]) {
						a[k + 2] = a[k];
					}
					a[++k + 1] = a1;

					while (a2 < a[--k]) {
						a[k + 1] = a[k];
					}
					a[k + 1] = a2;
				}
				double last = a[right];

				while (last < a[--right]) {
					a[right + 1] = a[right];
				}
				a[right + 1] = last;
			}
			return;
		}

		// Inexpensive approximation of length / 7
		int seventh = (length >> 3) + (length >> 6) + 1;

		/*
		 * Sort five evenly spaced elements around (and including) the center element in
		 * the range. These elements will be used for pivot selection as described
		 * below. The choice for spacing these elements was empirically determined to
		 * work well on a wide variety of inputs.
		 */
		int e3 = (left + right) >>> 1; // The midpoint
		int e2 = e3 - seventh;
		int e1 = e2 - seventh;
		int e4 = e3 + seventh;
		int e5 = e4 + seventh;

		// Sort these elements using insertion sort
		if (a[e2] < a[e1]) {
			double t = a[e2];
			a[e2] = a[e1];
			a[e1] = t;
		}

		if (a[e3] < a[e2]) {
			double t = a[e3];
			a[e3] = a[e2];
			a[e2] = t;
			if (t < a[e1]) {
				a[e2] = a[e1];
				a[e1] = t;
			}
		}
		if (a[e4] < a[e3]) {
			double t = a[e4];
			a[e4] = a[e3];
			a[e3] = t;
			if (t < a[e2]) {
				a[e3] = a[e2];
				a[e2] = t;
				if (t < a[e1]) {
					a[e2] = a[e1];
					a[e1] = t;
				}
			}
		}
		if (a[e5] < a[e4]) {
			double t = a[e5];
			a[e5] = a[e4];
			a[e4] = t;
			if (t < a[e3]) {
				a[e4] = a[e3];
				a[e3] = t;
				if (t < a[e2]) {
					a[e3] = a[e2];
					a[e2] = t;
					if (t < a[e1]) {
						a[e2] = a[e1];
						a[e1] = t;
					}
				}
			}
		}

		// Pointers
		int less = left; // The index of the first element of center part
		int great = right; // The index before the first element of right part

		if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
			/*
			 * Use the second and fourth of the five sorted elements as pivots. These values
			 * are inexpensive approximations of the first and second terciles of the array.
			 * Note that pivot1 <= pivot2.
			 */
			double pivot1 = a[e2];
			double pivot2 = a[e4];

			/*
			 * The first and the last elements to be sorted are moved to the locations
			 * formerly occupied by the pivots. When partitioning is complete, the pivots
			 * are swapped back into their final positions, and excluded from subsequent
			 * sorting.
			 */
			a[e2] = a[left];
			a[e4] = a[right];

			/*
			 * Skip elements, which are less or greater than pivot values.
			 */
			while (a[++less] < pivot1)
				;
			while (a[--great] > pivot2)
				;

			/*
			 * Partitioning:
			 *
			 * left part center part right part
			 * +--------------------------------------------------------------+ | < pivot1 |
			 * pivot1 <= && <= pivot2 | ? | > pivot2 |
			 * +--------------------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in
			 * (great, right) > pivot2
			 *
			 * Pointer k is the first index of ?-part.
			 */
			outer: for (int k = less - 1; ++k <= great;) {
				double ak = a[k];
				if (ak < pivot1) { // Move a[k] to left part
					a[k] = a[less];
					/*
					 * Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to
					 * performance issue.
					 */
					a[less] = ak;
					++less;
				} else if (ak > pivot2) { // Move a[k] to right part
					while (a[great] > pivot2) {
						if (great-- == k) {
							break outer;
						}
					}
					if (a[great] < pivot1) { // a[great] <= pivot2
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // pivot1 <= a[great] <= pivot2
						a[k] = a[great];
					}
					/*
					 * Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to
					 * performance issue.
					 */
					a[great] = ak;
					--great;
				}
			}

			// Swap pivots into their final positions
			a[left] = a[less - 1];
			a[less - 1] = pivot1;
			a[right] = a[great + 1];
			a[great + 1] = pivot2;

			// Sort left and right parts recursively, excluding known pivots
			sort(a, left, less - 2, leftmost);
			sort(a, great + 2, right, false);

			/*
			 * If center part is too large (comprises > 4/7 of the array), swap internal
			 * pivot values to ends.
			 */
			if (less < e1 && e5 < great) {
				/*
				 * Skip elements, which are equal to pivot values.
				 */
				while (a[less] == pivot1) {
					++less;
				}

				while (a[great] == pivot2) {
					--great;
				}

				/*
				 * Partitioning:
				 *
				 * left part center part right part
				 * +----------------------------------------------------------+ | == pivot1 |
				 * pivot1 < && < pivot2 | ? | == pivot2 |
				 * +----------------------------------------------------------+ ^ ^ ^ | | | less
				 * k great
				 *
				 * Invariants:
				 *
				 * all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great,
				 * *) == pivot2
				 *
				 * Pointer k is the first index of ?-part.
				 */
				outer: for (int k = less - 1; ++k <= great;) {
					double ak = a[k];
					if (ak == pivot1) { // Move a[k] to left part
						a[k] = a[less];
						a[less] = ak;
						++less;
					} else if (ak == pivot2) { // Move a[k] to right part
						while (a[great] == pivot2) {
							if (great-- == k) {
								break outer;
							}
						}
						if (a[great] == pivot1) { // a[great] < pivot2
							a[k] = a[less];
							/*
							 * Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be
							 * incorrect, if a[great] and pivot1 are floating-point zeros of different
							 * signs. Therefore in float and double sorting methods we have to use more
							 * accurate assignment a[less] = a[great].
							 */
							a[less] = a[great];
							++less;
						} else { // pivot1 < a[great] < pivot2
							a[k] = a[great];
						}
						a[great] = ak;
						--great;
					}
				}
			}

			// Sort center part recursively
			sort(a, less, great, false);

		} else { // Partitioning with one pivot
			/*
			 * Use the third of the five sorted elements as pivot. This value is inexpensive
			 * approximation of the median.
			 */
			double pivot = a[e3];

			/*
			 * Partitioning degenerates to the traditional 3-way (or "Dutch National Flag")
			 * schema:
			 *
			 * left part center part right part
			 * +-------------------------------------------------+ | < pivot | == pivot | ?
			 * | > pivot | +-------------------------------------------------+ ^ ^ ^ | | |
			 * less k great
			 *
			 * Invariants:
			 *
			 * all in (left, less) < pivot all in [less, k) == pivot all in (great, right) >
			 * pivot
			 *
			 * Pointer k is the first index of ?-part.
			 */
			for (int k = less; k <= great; ++k) {
				if (a[k] == pivot) {
					continue;
				}
				double ak = a[k];
				if (ak < pivot) { // Move a[k] to left part
					a[k] = a[less];
					a[less] = ak;
					++less;
				} else { // a[k] > pivot - Move a[k] to right part
					while (a[great] > pivot) {
						--great;
					}
					if (a[great] < pivot) { // a[great] <= pivot
						a[k] = a[less];
						a[less] = a[great];
						++less;
					} else { // a[great] == pivot
						/*
						 * Even though a[great] equals to pivot, the assignment a[k] = pivot may be
						 * incorrect, if a[great] and pivot are floating-point zeros of different signs.
						 * Therefore in float and double sorting methods we have to use more accurate
						 * assignment a[k] = a[great].
						 */
						a[k] = a[great];
					}
					a[great] = ak;
					--great;
				}
			}

			/*
			 * Sort left and right parts recursively. All elements from center part are
			 * equal and, therefore, already sorted.
			 */
			sort(a, left, less - 1, leftmost);
			sort(a, great + 1, right, false);
		}
	}
}
